1. ## Limits...

hey i have a question about a limit problem. i tried putting values less than 0 i.e. .1, .01, .001...and so on but it didnt seem to work...help?

lim as x-->theta of theta/tan(4theta)

thanks...

2. Originally Posted by mer1988
hey i have a question about a limit problem. i tried putting values less than 0 i.e. .1, .01, .001...and so on but it didnt seem to work...help?

lim as x-->theta of theta/tan(4theta)

thanks...
Be sure you are in radians.

$\displaystyle \left\{ \begin{array}{cc} \theta & \frac{\theta}{\tan (4\theta)} \\ 1 & .8637 \\.1 & .2365 \\ .01 & .2499 \\ .001& .2500 \end{array} \right.$

So what do you think it is?

3. Originally Posted by ThePerfectHacker
Be sure you are in radians.

$\displaystyle \left\{ \begin{array}{cc} \theta & \frac{\theta}{\tan (4\theta)} \\ 1 & .8637 \\.1 & .2365 \\ .01 & .2499 \\ .001& .2500 \end{array} \right.$

So what do you think it is?

those are the outcomes for the values less than zero and the other thing is like a limit def. or something

4. Originally Posted by mer1988
hey i have a question about a limit problem. i tried putting values less than 0 i.e. .1, .01, .001...and so on but it didnt seem to work...help?

lim as x-->theta of theta/tan(4theta)

thanks...
Try this:
$\displaystyle \lim_{\theta \to 0}\frac{\theta}{tan(4\theta)}$

Change the variable to $\displaystyle \alpha = 4 \theta$. Then $\displaystyle \alpha \to 0$ as $\displaystyle \theta \to 0$. Thus

$\displaystyle \lim_{\theta \to 0}\frac{\theta}{tan(4\theta)} = \lim_{\alpha \to 0}\frac{\frac{1}{4} \alpha}{tan(\alpha)} = \frac{1}{4} \cdot \lim_{\alpha \to 0}\frac{\alpha}{tan(\alpha)}$

Does this help?

-Dan

5. Originally Posted by topsquark
Try this:
$\displaystyle \lim_{\theta \to 0}\frac{\theta}{tan(4\theta)}$

Change the variable to $\displaystyle \alpha = 4 \theta$. Then $\displaystyle \alpha \to 0$ as $\displaystyle \theta \to 0$. Thus

$\displaystyle \lim_{\theta \to 0}\frac{\theta}{tan(4\theta)} = \lim_{\alpha \to 0}\frac{\frac{1}{4} \alpha}{tan(\alpha)} = \frac{1}{4} \cdot \lim_{\alpha \to 0}\frac{\alpha}{tan(\alpha)}$

Does this help?
Is not necessary to set a change of variable

$\displaystyle \lim_{\theta\to0}\frac\theta{\tan4\theta}=\frac14\ lim_{\theta\to0}\frac{4\theta}{\tan4\theta}$

Then it's done...

6. Originally Posted by Krizalid
Is not necessary to set a change of variable

$\displaystyle \lim_{\theta\to0}\frac\theta{\tan4\theta}=\frac14\ lim_{\theta\to0}\frac{4\theta}{\tan4\theta}$

Then it's done...
(snort!) I always do things the hard way...

-Dan